       The 2D Riemann problem of gas dynamics is proposed in
[1]} and solved on the rectangular domain \([0,1]\times [0,1]\) .
The 2D Riemann problem is defined by initial constant states in each
quadrant which is divided by lines \(x=0.8\)  and \(y=0.8\)  on the square
as
\((\rho ,u,v,p) & ={\left\lbrace \begin{array}{ll}\begin{array}{lr}(1.5,0,0,1.5) & if\;0.8\le x\le 1,0.8\le y\le 1,\\(0.5323,1.206,0,0.3) & if\;0\le x<0.8,0.8\le y\le 1,\\(0.138,1.206,1.206,0.029) & if\;0\le x<0.8,0\le y<0.8,\\(0.5323,0,1.206,0.3) & if\;0.8<x\le 1,0\le y\le 0.8,\end{array}\end{array}\right.}\) 
